Abelian and Non-Abelian Branes in WZW Models and Gerbes
Abelian and Non-Abelian Branes in WZW Models and Gerbes
复制标题
WZW 模型和 Gerbe 中的阿贝尔膜和非阿贝尔膜
DOI：
10.1007/s00220-005-1301-1
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发表时间：
2004
影响因子：
2.4
通讯作者：
K. Gawȩdzki
中科院分区：
文献类型：
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作者：
K. Gawȩdzki
我们讨论了如何使用GERBS来建立一个一致的拉格朗日方法来求解带边界的WZW模型。该方法允许详细研究可能的边界条件，这些边界条件将世界表边界上的场值限制在目标组中的膜子流形上。这些子流形配备了附加的几何结构，该几何结构可概括为Gerbe模的概念，并且包括扭曲的Chan-Paton规范场。利用几何方法，我们给出了WZW模型中保持对角电流代数对称性的膜的完整分类，这些膜具有简单、紧凑但不一定是简单连接的靶群。这种对称膜由目标群中的一系列离散的共轭类支撑，并且可以携带阿贝尔或非阿贝尔扭曲规范场。对于基本群为ℤ_2×ℤ_2inSO(4N)/ℤ_2的共轭类，出现后一种情况。在两种不同于离散挠率的可能的WZW模型中，被这种共轭类支撑的膜必须配备一个射影平坦的双U(2)规范场。我们展示了膜的几何描述如何导致具有非单连通目标群的WZW模型中边界配分函数和边界算符乘积系数的显式公式。
We discuss how gerbes may be used to set up a consistent Lagrangian approach to the WZW models with boundary. The approach permits to study in detail possible boundary conditions that restrict the values of the fields on the worldsheet boundary to brane submanifolds in the target group. Such submanifolds are equipped with an additional geometric structure that is summarized in the notion of a gerbe module and includes a twisted Chan-Paton gauge field. Using the geometric approach, we present a complete classification of the branes that conserve the diagonal current-algebra symmetry in the WZW models with simple, compact but not necessarily simply connected target groups. Such symmetric branes are supported by a discrete series of conjugacy classes in the target group and may carry Abelian or non-Abelian twisted gauge fields. The latter situation occurs for the conjugacy classes with fundamental group ℤ2×ℤ2inSO(4n)/ℤ2. The branes supported by such conjugacy classes have to be equipped with a projectively flat twistedU(2) gauge field in one of the two possible WZW models differing by discrete torsion. We show how the geometric description of branes leads to explicit formulae for the boundary partition functions and boundary operator product coefficients in the WZW models with non-simply connected target groups.
物理学家的拓扑、范畴论和微分几何
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
S.;Tanimura
通讯作者：
Tanimura